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We study the interactions between a protostar and its circumstellar discunder the influence of an external binary companion to determine the evolutionof the mutual stellar spin - disc misalignment angle. The gravitational torqueon the disc from an inclined binary makes the disc precess around the binaryaxis, while the star-disc interaction torque due to the rotation-inducedquadrupole makes the stellar spin and the disc angular momentum axes precessaround each other. A significant star-disc misalignment angle can be generatedfrom a small initial value as the star-disc system evolves in time such thatthe two precession frequencies cross each other. This ``secular resonance''behavior can be understood in a geometric way from the precession dynamics ofspin and disc angular momenta. We derive the conditions for such resonance tooccur, and find that they can be satisfied for reasonable protostar-disc-binaryparameters. The evolution of star-disc inclination is also affected by massaccretion and by magnetic star-disc interaction torques, which can eitherpromote or reduce star-disc misalignment. In general, as long as the initialbinary-disc inclination is greater than a few degrees, a variety of star-discmisalignment angles can be generated within the disc lifetimes. We discuss theimplications of our results for the stellar spin orientations in binaries, forthe alignments/misalignments of protostellar discs and debris discs, and forthe stellar obliquities in exoplanetary systems. In particular, if hot Jupitersare produced by the Kozai effect induced by an external stellar companion, thenit is likely that ``primordial'' star-disc misalignments are already generatedby the star-disc-binary interactions. Even for systems where the Kozai effectis suppressed, misaligned planets may still be produced during theprotoplanetary disc phase.

Star-Disc-Binary Interactions in Protoplanetary Disc Systems and Primordial Spin-Orbit Misalignments